Find in how many ways can (i) at least one fruit be selected ? (ii) one fruit of each type be selected? (iii) at least one fruit of each type be selected ? Grom 5 organs, 7 mangoes and 8 bananas?

Find in how many ways can (i) at least one fruit be selected ? (ii)

1.	Find in how many ways can (i) at least one fruit be selected ? (ii) one fruit of each type be selected? (iii) at least one fruit of each type be selected ? Grom 5 organs, 7 mangoes and 8 bananas?
Answer» Solution :(i) No. of ways of selecting at least one fruit `= (5 +1) (7+1) (8+1)-1` `= 6 XX 8 xx 9 - 1` `= 432 - 1 = 431` (ii) No. of ways of selecting one fruit of each type `=.^(5)C_(1) xx .^(7)C_(1) xx.^(8)C_(1) = 5 xx 7 xx 8 = 280`. (iii) No. of ways of selecting at least one orange `= 2^(5) - 1 = 31` No. of ways of selecting at least one mango `= 2^(7) - 1 = 127` No. of ways of selecting at least one banana `= 2^(8) - 1 = 255` `:.` No. of ways of selecting at least one fruit of each type `= 31 xx 127 xx 255 = 1003935`